One of the first waves of protest against the scale of government budget cuts is due to wash across the UK tomorrow, with Vodafone bearing the brunt after a week of allegations and demonstrations.

Protesters say hundreds of people will be involved in the anti-cuts protests across 10 cities, which will target the mobile telecoms company's stores.

On Wednesday about 60 activists shut down Vodafone's store on Oxford Street, central London, handing out flyers which accused the company of avoiding paying £6bn in taxes – a claim which the company and HM Revenue and Customs (HMRC) deny.

Tomorrow's follow-up protests will, activists promise, have even greater impact. "It's gone from a conversation between a group of people who didn't really know what they were doing to action in eight cities," said Tom Costello, a 22-year-old TV researcher from Lewisham, south-east London.

A Vodafone spokesman referred to the allegations as "an urban myth", while a statement on the company's website insisted that the company "meets its tax obligations in the UK" and was paying the full £1.25bn sum of tax agreed following the HMRC's investigation.

A spokesman for the tax collector insisted that he could not comment on the detail of the settlement, "but we can confirm that it was reached by HMRC following a rigorous examination of the facts and an intensive process of negotiation that tested the arguments of both parties."

There was no question of Vodafone having an outstanding tax bill of £6bn, he added.

The assertions seem unlikely to halt tomorrow's action, with demonstrations being planned in up to 10 cities, including Bournemouth, Liverpool, Hastings, York, Glasgow, Edinburgh and Leeds – where three stores were forced to close the day after the London protest this week.

Costello said the protests would follow a similar format to Wednesday when about 65 activists entered the Vodafone store and sat on the floor, blockading the entrance. Police moved them outside, where some continued their sitting protest while others handed out anti-cuts leaflets. The branch was closed from 10am until 3.30pm.

"The response from the public was really what motivated us to do this again," said Ed Thompson, 25, who was at the protest.